This work introduces a new simple approach to determine experimental X-ray elastic constants (XECs) of thin films by coupling the sin2ψ method and the substrate curvature technique. The approach is demonstrated on polycrystalline Cu thin films with the thickness 200, 800, and 2400 nm deposited on Si(100) substrates. Applying synchrotron radiation, the elastic strains in the films are determined using sin2ψ method while the macroscopic stresses are assessed by measuring the substrate curvature. The stresses are calculated using the Stoney formula from the radius of substrate curvature determined by the rocking curve measurement of substrate 400 reflection at different sample positions. Results show that the magnitude of the macroscopic stress in the films is proportional to the magnitude of the slope in the sin2ψ plots. On the basis of this observation, XECs of the films were calculated showing no dependence on the film thickness. The characterization of the samples was performed at the synchrotron source Hasylab.